Mexico City, Mexico (CNN) -- The Mexican government has apologized to the families of two students killed early Friday who officials initially said were drug gang members.

Jorge Antonio Mercado Alonso, 23, and Javier Francisco Arredondo Verdugo, 24, were mechanical engineering graduate students at the Technological Institute of Higher Learning of Monterrey, the Mexican Interior Ministry said Sunday in its apology for the shootings.

Mexican soldiers chasing criminals who had fired on an army patrol shot and killed the students, the Interior Ministry said. Some of the criminals had fled onto the college campus.

"The Mexican government expresses its most deeply felt condolences to the families," the Interior Ministry said in a release on its Web page.

The federal government will intensify its investigation to find out what happened, the ministry said.

On Friday, Mexican officials had said the two dead men were part of the criminal gang that shot at the soldiers. University officials also said Friday that all students were safe.

That account changed Saturday, when Mercado's mother tried to call him after finding out about the campus shootout. When she couldn't reach him, she traveled to Monterrey, where she identified her son's body, said the campus rector, Rafael Rangel Sostman.

"I'm certain he is with God," said the mother, Rosa Elvia Mercado Alonso.

The school's rector blamed himself for the mix-up in identities.

"I offer a public apology and take responsibility for having given information that ended up not being correct," Rangel said. "I want to offer my most deeply felt condolences to the family of our two students and offer them our support in this difficult situation."

Both men were scholarship students, the college said.

Monterrey is in Nuevo Leon, one of two states in northeastern Mexico where drug cartel members blocked roads with hijacked vehicles Thursday and Friday to prevent military reinforcements from arriving. The criminals also set up roadblocks in neighboring Tamaulipas state.

Three presumed gang members and one soldier were killed in various skirmishes over the two-day period, officials said.

The area, which borders Texas, has seen bloody fighting between the Zetas and Gulf cartels after a recent gangland slaying. Hours-long gun battles are common, and U.S. officials were recently forced to temporarily close the consulate in the city of Reynosa.

Mexico has been gripped in massive drug-related bloodshed since President Felipe Calderon declared war on the cartels shortly after coming into office in December 2006. Much of the violence has taken place around Ciudad Juarez, across the border from El Paso, Texas.

There are no official government tallies, but more than 16,000 people are estimated to have died in the drug wars. The vast majority of the deaths are among reputed criminals, with some police and military also being killed. Relatively few of the deaths have been civilians.

Even so, the United States and Canada have issued travel warnings, particularly along the border area. The Texas Department of Public Safety took the unprecedented step this year of recommending that students on spring break not go to border areas inside Mexico.

News of the violence and the travel warnings apparently have had an effect. Mexicans say tourism along the border has declined significantly this year.